# jtms88

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# 76 Questions

 13 Finding $\displaystyle \lim_{n \to \infty} \int_0^\infty \frac{e^{-x}\cos{x}}{nx^2 + \frac{1}{n}}dx$ 11 Determine $\displaystyle \lim_{n \to \infty}{{n} \choose {\frac{n}{2}}}\frac{1}{2^n}$, where each $n$ is even 8 Show that a proper continuous map from $X$ to locally compact $Y$ is closed 8 Give an example of two closed sets $A, B \subseteq \mathbb{R}$ such that the set $A + B$ is not closed [duplicate] 6 Approximation of a harmonic function on the unit disc by harmonic polynomials.

# 1,044 Reputation

 +10 Show that a proper continuous map from $X$ to locally compact $Y$ is closed +5 computing how distributional derivatives behave under coordinate transformations +5 Understanding connectedness argument in proof of Analytic Fredholm Theorem +5 Show that a positive operator on a complex Hilbert space is self-adjoint

 9 Cauchy sequences - can we control the rate at which elements “get closer”? 1 Question about different defintions of isometry on a Hilbert space 1 For all $f: D_1(0) \to D_1(0)$ analytic with $f(\frac{i}{3}) = 0$, find $\displaystyle \sup_f\{\operatorname{Im} f(0) \}$ 1 If we anti-differentiate the Laurent series $\sum_{n=2}^{\infty} a_n(z - a)^{-n}$, how is the radius of convergence affected? 1 Show that analytic function $f$ cannot be conformal when $f'(z) = 0$

# 36 Tags

 10 real-analysis × 12 1 hilbert-spaces × 9 9 cauchy-sequences 0 measure-theory × 8 3 complex-analysis × 22 0 linear-algebra × 5 1 functional-analysis × 22 0 topological-vector-spaces × 5 1 pde × 11 0 general-topology × 5

# 1 Account

 Mathematics 1,044 rep 412